Full scale measurements of the resistance and powering coeffiecients and the resulting improvement in the extrapolation process from model to ship

P P - 4

M.A. A B K O W I T Z

Massachussetts Institute of Technology, U.S.A,

F U L L S C A L E M E A S U R E M E N T S O F T H E R E S I S T A N C E A N D P O W E R I N G C O E F F I C I E N T S A N D T H E R E S U L T I N G I M P R O V E M E N T IN T H E E X T R A P O L A T I O N P R O C E S S F R O M M O D E L T O S H I P

The goal of the towing tank establishments is to predict ship performance from design features (geometry/shape). Since "mathematical models" (Iheorclical hydrodynamics) arc still very limited in their capability to satisfactorily perform this prediction, wc must still rely (for quite a while yet) on scaled "physical models" tested in the towing tank. As is well known, the hydrodynamic coefficients involved in resistance and powering suffer from "scale effects" because of the inability in the model test to satisfy the viscous parameter of Reynolds' number.

In order to predict a power-speed relationship for the ship, several model tests are carried out to measure the resistance coefficient (smooth hull) ( C J , the wake fraction (w), the thrust deduction factor (t), and the propeller thrust (K^) and torque (K^) coefficients in both open water and self-propelled conditions. These five coefficients are all functions of Reynolds' number and therefore suffer f r o m "scale effects". To these a si.xth coefficient in the form of roughness factor (ACp) must be estimated for the ship f r o m hydrodynamic phenomena measured at low model test Reynolds' number.

In the process of predicting ship power performance from model test, six different factors must be extrapolated from model tests or predicted f r o m some hydrodynamic basis, all of which suffer from "scale effects".

predicted power = / [ ( C ^ + AC^), w, t, Kj, K^^

(1) When measured power from ship trials are compared to that predicted f r o m model tests,

( 1 ) i f there is an error in the prediction, then one or more of the coefficients may have been wrongly prcdicted.The standard culprit in the past was the roughness factor (ACj.) until negative roughness factors appeared when there was a significant change in ship size and fullness. In reality, the roughness factor has represented a roughness in the extrapolation process rather than specifically the ship roughness.

(2) i f there is an agreement between actual ship power and that predicted from model tests, all of the coefficients may have been properly predicted or several of the coefficients may have been wrongly predicted w i t h errors in some o f the coefficients compensating f o r errors in other coefficients. In the latter case, one may build up confidence in a faulty prediction procedure in that compensating errors may only exist for that particular ship geometry and the agreement would be fortuitous. It probably would not work w e l l for a different ship and/or propeller geometry.

A t M I T , wc have developed special procedures o f system identification whereby (Q+ACp), w , t and K j (open water) can be "measured" (identified) on the ship from simple acceleration-deceleration trials carried out during a regularly scheduled voyage using instruments normally on board. Records o f t h e fonvard speed (reliably measured by Dopplcr or similar speed log) and the propeller R P M during the trial provide the necessary data for sy.stcm identification analysis. The measurement of rudder angle and heading are made to assure that the ship is moving straight ahead w i t h negligible rudder action. I f shaft horsepower (SHP) is measured, then KQ can also be determined.

These tests were carried out on a routine voyage between Valdez, Alaska and San Francisco and ( C R + A C , , ) , W , t and of the ship were successfully identified. These trials are reported in Reference I . More recently, similar trials on a U.S. Navy submarine were analyzed w i t h the M I T system identification technique and the successful results arc reported in Reference 2. Within a few months, these trials w i l l be performed on one of the American President Lines' new large fast container ships on a routine voyage between Los Angeles and San Francisco.

We are now in the position to measure f u l l scale (C^ +ACp), w , t, K T and KQ and thereby provide a basis on which to extrapolate each o f these factors f r o m model to f u l l scale. This should provide a marked improvement in the ability to predict ship performance i n the area of ship resistance and powering. Reasonable extrapolation methods f o r wake fraction (w) and thrust deduction factor (t) are shown in Figures 1 through 4 using data obtained f r o m the trials of the tanker and submarine.

In Figure I , the model measured value and the ship identified values of w for the tanker are plotted against the plank friction coefficient C^- (inverse of log Reynolds' no.) on a background o f test data from several different geosim scries of models. Since Cp = 0 represents infinite Reynolds' no. (zero viscosity), potential f l o w calculations w i l l give the value o f w since there is no frictional wake and the trials are run below wavemaking speed. A faired curve between the values at model Reynolds' no., ship Reynolds' no. and infinite Reynolds' no. would provide a basis for the extrapolation of w for that type of ship. The model test value for w and the potential w can be obtained for a model of a new desing and a curve between these two points drawn parallel (or in a similar shape) to the faired curve previously developed would provide a predicted value for w for the ship at the Reynolds' no. at which the ship is to operate. Notice how the model test and the ship identified values of w would lie on a curve which is reasonably parallel to the geosim curves. Figure 2 shows a similar curve for the submarine. Unfortunately, the potential wakes for the tanker and the submarine have not been calculated.

0 . 2 A -E X X O H P H I L A D -E L P H I A M O D E L 0 V I C T O R Y Ó T A N K E R • T A N K E R 5 C , i t o 3

Fig. 1 Wake fraction o f geosims as a function of Cf

SL'B>UP.INE

Fig. 2 Wake fraction a.s a function o f Cf

T A N K E P / a L U N T STEHfJ WITH

f i X f O S E P A n A n O N POINT FOB

LONG FiAfiGE OF BEVNOLDS NO. NO FRCUDE EFFECTS

A t infinite Reynolds' no. (Cy = 0) the f l o w is ideal and the resistance is zero ( i f below wavemaking speed) according to D'Alembert's paradox. Therefore, for all shios t = 1 at infinite Reynolds' no.. In Figures 3 and 4, there are three points on which to perform the extrapolation curve for t. The extrapolation process for t would be similar to that described for w.

S U D M A n l f l t - T A P É RED STERN Wl TM • SEPARATION POINT MOVING

A F T WITH INCREASING REYNOLDS" NO

F R U j n n N A L r . d F P F l C I F N I C,

Fig. 4 Thrust deduction factor vs Cf

FRICTIONAL COEFPICIENI C, « 10

Fig. 3 Thrust deduction factor vs Cf

In Figures 3 and 4, the thrust deduction factor (t) is plotted vs. Cp for the tanker and submarine respectively. The definition of t is given by

thrust ( I - t) = resistance

Since (CR + ACp) for the ship is identified, we are in a much better position to improve our methods of extrapolation of model resistance to f u l l size. The resistance coefficient for the tanker was over predicted by greater than 12% and the resistance coefficient o f the submarine was over predicted by 10%. This error can be specifically attributed to the prediction of CR and ACp. We can now clearly focus our investigation

of resistance scale effects on three possible contributors.

1. an inaccurate estimate of plank frictional resistance (Cp) at ship Reynolds' no. where there is no reliable data - only a lengthy extrapolation from scattered data at a much lower Rcynold.s' no.

2. an inaccurate method of extrapolating the eddy resistance from model to full scale.

3. an error in the estimate of the ship roughness factor, ACp.

Present methods of extrapolation tend toward compensating errors in the prediction of Cp and ACp.

References

[1] "Mea.surement of Ship Resistance, Powering and Manoeuvering Coefficients from Simple Trials During a Regular Voyage", Martin A . Abkowitz and Gengshen Liu, Transactions of Society of Naval Architects and Marine Engineers, November 1988.

[2] "Measurement of Resistance and Powering Coefficients of the Tanker E X X O N P H I L A D E L P H I A and a Navy Submarine from Simple Full-Scale Trials and Their Implications in Ship Performance Prediction from Model Tests", Martin A . Abkowitz, New England Section of S N A M E , January 1990.

P P - 5

K . R . S U H R B I E R

Vosper Thornycroft ( U K ) Limited, U . K .

ON H I G H - S P E E D C R A F T

1 would like to congratulate the Committee to their interesting and balanced report and wish to make a few comments:

As referred to, power prediction procedures for high-speed craft are also discussed by the H S M V Committee and the conclusions and proposals of both committees seem to be largely in agreement. It may be perhaps added that it is certainly not ea.sy, or even impo.ssible, to define simple straight-forward procedures for all types of high-speed craft. Amongst other influences, cavitation and ventilation can considerably complicate matters; not only propeller efficiency but also thrust deduction, trim and thus resistance, etc. can be affected. Such phenomena arc often difficult to allow for unless additional, more complex, investigations are carried out.

As regards scale effects on appendage resistance, obviously a subject of great importance for high-speed craft predictions, the H S M V Committed reached rather similar conclusions, namely that the p factor correction procedure or extrapolations based on a form factor method are - at present - the most practical approaches, particularly for bluff bodies, such as open inclined propeller shafts. For other appendages, corrections can usually also be based on calculations (formulae) with a reasonable degree of accuracy.